I'm experimenting with rolling back my 8-key C foot to keep the Eb key under my RH4 finger. Before this, I was rolling that foot out, because I don't really need that Eb key for many tunes, and hey; if it's good enough to roll that C foot out for Matt Molloy and Kevin Crawford, it's good enough for me.
But then I realized (because (I also play mandolin) that there are enough tunes that use the Eb key that I really should try resting my RH4 finger on the Eb key, or at least letting it fly out in space so it's not harming the D note. The latest challenge is Beare Island... ugh, that's a killer with a lot of D# and Eb notes. But I love that tune, and except for the low note that I can fake, I should be able to play it on flute.
Without the E4 (pinky) finger helping to support the flute like I was used to, I instinctively raised my RH thumb a little upward on the barrel for a 3-point support (under-chin, side of LH index finger, RH thumb against the flute).
That's when I realized that I had some help with my RH thumb.
I play fingerstyle guitar as well as flute and mandolin, and I've always tried to keep a fairly long, healthy RH thumb nail. That extra length of nail is a PERFECT help in supporting the flute. It's a little bit of extra leverage below the tip of the thumb that can sit underneath the flute barrel. See image below.
I have no idea if this will be useful to anyone else, and it's a fragile thing to depend on. I've ripped off that thumbnail many times in the past and had to grow it back. It's not something to depend on, but right now it's useful. Maybe some future flute historian will look at this flute and try to figure out why there is a scratch mark under the barrel.